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author | Karl Berry <karl@freefriends.org> | 2021-04-11 21:10:56 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2021-04-11 21:10:56 +0000 |
commit | 1d2e2ac9a87fc3f31456f44714e1f6afd2945b6d (patch) | |
tree | c44a3cf769f7cf05f43491df5d4b2d11b988a8a1 /Master/texmf-dist/doc/latex/easybook/chapter2.tex | |
parent | 3d3efb1f22048b945c97b8c68967616dba0fb78e (diff) |
easybook (11apr21)
git-svn-id: svn://tug.org/texlive/trunk@58832 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/easybook/chapter2.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/easybook/chapter2.tex | 8 |
1 files changed, 4 insertions, 4 deletions
diff --git a/Master/texmf-dist/doc/latex/easybook/chapter2.tex b/Master/texmf-dist/doc/latex/easybook/chapter2.tex index cee689e4d43..d72ee6424a6 100644 --- a/Master/texmf-dist/doc/latex/easybook/chapter2.tex +++ b/Master/texmf-dist/doc/latex/easybook/chapter2.tex @@ -19,7 +19,7 @@ \\ & =\oiint_\Sigma \left(P\cos\alpha + Q\cos\beta + R\cos\gamma\right)\mathrm{d}S \end{align} -这里$\Sigma$是整个边界曲面$\Omega$的外侧,$\cos\alpha,\cos\beta,\cos\gamma$是$\Sigma$在点$(x,y,z)$处的法向量的方向余弦。引用这个公式如\cref{theorem:gauss formula}。 +这里$\Sigma$是整个边界曲面$\Omega$的外侧,$\cos\alpha,\cos\beta,\cos\gamma$是$\Sigma$在点$(x,y,z)$处的法向量的方向余弦。引用这个公式如\ref{theorem:gauss formula}。 \end{theorem} \begin{definition}[(Stokes formula)] @@ -68,11 +68,11 @@ The Stokes formula is an extension of the basic calculus formula in the case of \zhlipsum*[3][name = aspirin] \begin{exercise}[LightYellow][1.](习题) \index{x@习题环境} - \item 设$w = f(x + y + z,xyz)$,$f$具有二阶连续偏导数,求$\dfrac{{\partial w}}{{\partial x}}$和$\dfrac{{{\partial ^2}w}}{{\partial x\partial z}}$。 + \item 设$w = f(x + y + z,xyz)$,$f$具有二阶连续偏导数,求$\dfrac{\partial w}{\partial x}$和$\dfrac{\partial ^2 w}{\partial x\partial z}$。 \item 已知$y = y(x)$在任意点$x$处的增量$\Delta y = \dfrac{y\Delta x}{1 + x^2} + \alpha$,其中$\alpha$是$\Delta x$的高阶无穷小($\Delta x\to 0$时),$y(0) = \pi$,则$y(1) = \uline{\mbox{\hspace{2em}}}$。 - \item 设函数$f(x)$在$( - \infty, + \infty)$上有定义,则下述命题中正确的是 \mbox{(\hspace{1.5em})} + \item 设函数$f(x)$在$(-\infty,+\infty)$上有定义,则下述命题中正确的是 \mbox{(\hspace{1.5em})} \begin{tasks} - \task 若$f(x)$在$( - \infty, + \infty)$上可导且单调增加,则对一切$x\in ( - \infty, + \infty)$,都有$f'(x) > 0$。 + \task 若$f(x)$在$(-\infty,+\infty)$上可导且单调增加,则对一切$x\in (-\infty,+\infty)$,都有$f'(x) > 0$。 \task 若$f(x)$在点$x_0$处取得极值,则$f'(x_0) = 0$。 \task 若$f''(x_0) = 0$,则$(x_0,f(x_0))$是曲线$y = f(x)$的拐点坐标。 \task 若$f'(x_0) = 0$, $f''(x_0) = 0$,$f'''(x_0)\ne 0$,则$x_0$一定不是$f(x)$的极值点。 |